Modelling the nonlinear behaviour of double walled carbon nanotube based resonator with curvature factors

This paper deals with the nonlinear vibration analysis of a double walled carbon nanotube based mass sensor with curvature factor or waviness, which is doubly clamped at a source and a drain. Nonlinear vibrational behaviour of a double-walled carbon nanotube excited harmonically near its primary resonance is considered. The double walled carbon nanotube is harmonically excited by the addition of an excitation force. The modelling involves stretching of the mid plane and damping as per phenomenon. The equation of motion involves four nonlinear terms for inner and outer tubes of DWCNT due to the curved geometry and the stretching of the central plane due to the boundary conditions. The vibrational behaviour of the double walled carbon nanotube with different surface deviations along its axis is analyzed in the context of the time response, Poincaré maps and Fast Fourier Transformation diagrams. The appearance of instability and chaos in the dynamic response is observed as the curvature factor on double walled carbon nanotube is changed. The phenomenon of Periodic doubling and intermittency are observed as the pathway to chaos. The regions of periodic, sub-harmonic and chaotic behaviour are clearly seen to be dependent on added mass and the curvature factors in the double walled carbon nanotube. Poincaré maps and frequency spectra are used to explicate and to demonstrate the miscellany of the system behaviour. With the increase in the curvature factor system excitations increases and results in an increase of the vibration amplitude with reduction in excitation frequency.     

Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities

The present study is concerned with the design of a new type of single degree of freedom (sdof) nonlinear vibration isolation system that can deal with harmonic excitations and take advantage of both spring and damping nonlinearities. For typical design requirements expressed in terms of a transmissibility envelope, the proposed design makes use of a recently developed method called the output frequency response function (OFRF) approach, which provides a direct relationship between the system output frequency response and parameters that define the system nonlinearity. Taking all output harmonics into account, a detailed step-by-step procedure is developed to systematically determine the nonlinear parameters from a small set of simulation or experimental data. Simulation studies are conducted to verify the results and demonstrate that the design can effectively achieve all the three requirements for a vibration isolation system of a low resonant peak, low high frequency transmissibility, and a large isolation range.     

Dynamic analysis of double-row self-aligning ball bearings due to applied loads,internal clearance,surface waviness and number of balls

In this paper, a three degrees of freedom (dof) model was established for a double-row self-aligning ball bearing (SABB) system, and was applied to study the dynamic behavior of the system during starting process and constant speed rotating process. A mathematical model was developed concerning stiffness and damping characteristics of the bearing, as well as three-dimensional applied load, rotor centrifugal force, etc. Balls and races were all considered as nonlinear springs, and the contact force between ball and race was calculated based on classic Hertzian elastic contact deformation theory and deformation compatibility theory. The changes of each ball?s contact force and loaded angle of each row were taken into account. In order to solve the nonlinear dynamical equilibrium equations of the system, these equations were rewritten as differential equations and the fourth order Runge–Kutta method was used to solve the equations iteratively. In order to verify accuracy of the dynamical model and correctness of the numerical solution method, a kind of SABB-BRF30 was chosen for case studies. The effects of several important governing parameters, such as radial and axial applied loads, normal internal, inner and outer races waviness, and number of balls were investigated. These parametric studies led to a complete characterization of the shaft-bearing system vibration transmission. The research provided a theoretical reference for new type bearing design, shaft-bearing system kinetic analysis, optimal design, etc.     

Improved model of a ball bearing for the simulation of vibration signals due to faults during run-up

In this paper an improved bearing model is developed in order to investigate the vibrations of a ball bearing during run-up. The numerical bearing model was developed with the assumptions that the inner race has only 2 DOF and that the outer race is deformable in the radial direction, and is modelled with finite elements. The centrifugal load effect and the radial clearance are taken into account. The contact force for the balls is described by a nonlinear Hertzian contact deformation. Various surface defects due to local deformations are introduced into the developed model. The detailed geometry of the local defects is modelled as an impressed ellipsoid on the races and as a flattened sphere for the rolling balls. With the developed bearing model the transmission path of the bearing housing can be taken into account, since the outer ring can be coupled with the FE model of the housing. The obtained equations of motion were solved numerically with a modified Newmark time-integration method for the increasing rotational frequency of the shaft. The simulated vibrational response of the bearing with different local faults was used to test the suitability of the envelope analysis technique and the continuous wavelet transformation was used for the bearing-fault identification and classification.     

阶梯圆环压电超声换能器径向振动性能的理论研究*

提出了一种阶梯圆环径向振动压电超声换能器,根据力电类比原理建立了阶梯圆环及阶梯圆环换能器的径向振动等效电路,推导了阶梯圆环的径向共振频率方程和位移放大系数,在此基础上进一步推导了换能器的径向共振和反共振频率方程。通过理论推导和有限元仿真模拟分析了阶梯圆环压电超声换能器的径向振动性能。结果表明,增大阶梯圆环中内外环的径向厚度之比K1或减小轴向厚度之比K2,阶梯圆环的一阶径向共振频率减小,二阶径向共振频率增大;在二阶径向共振模式下,K1、K2值在一定范围内阶梯圆环可实现由内向外的径向位移振幅放大;随着压电陶瓷圆环的内半径增大,阶梯圆环压电超声换能器的一阶、二阶径向共振和反共振频率减小,二阶径向共振下的有效机电转换系数趋于零;增大阶梯圆环内环的外半径,换能器的一阶径向共振和反共振频率减小,二阶径向共振和反共振频率先增大后减小,理论推导与仿真模拟结果符合良好。本文研究结果为阶梯圆环压电超声换能器的工程应用提供理论参考。     

The simulation of random vibration response by discrete frequency testing

The paper presents the theoretical basis for an analogue method whereby the random response of a structure may be inferred from measurements of its harmonic response when the excitations are replaced by discrete frequency forces or imposed motions. In the elementary case of a single random input, the method takes a particularly simple form. In the general multi-input case it is shown that the method may be used directly only when all the inputs are fully coherent. Otherwise a superposition technique involving multiple applications of sets of harmonic excitations is required. It is considered that the method may be of practical use as a tool in vibration testing and that, in addition, the underlying analysis contains results of considerable interest on the structure of multi-dimensional stationary random processes.     

Noise rejection for two time-based multi-output modal analysis techniques

Modal analysis is a well-developed field with many applications. In particular, forced response multi-output approaches are well suited for system identification and online damage detection because they use the natural excitations the system undergoes during its normal operation. In this work, two of these approaches, smooth orthogonal decomposition (SOD) and direct system parameter identification (DSPI), are analyzed, compared, and improved upon. SOD was originally developed as a tool for detecting features of chaotic dynamical systems. Recently, it has been used as a time-based multi-output modal analysis approach. SOD has been demonstrated to work for the free vibration case and for random excitations. DSPI was developed as a time-based multi-input multi-output approach. When the inputs are not measured, DSPI is very similar to SOD and can handle both free vibrations and random excitations. However, if the inputs are measured or known DSPI can also handle arbitrary excitations. To improve the performance of these two methods when used with noisy data, novel noise filtering algorithms are proposed. Numerical simulations are performed to compare the two methods and to show the effectiveness of the filtering algorithms in improving frequency and mode shape extraction.     

Observations of changes in acoustic emission waveform for varying seeded defect sizes in a rolling element bearing

The investigation reported in this paper was centered on the application of the acoustic emissions (AE) technology for characterising the defect sizes on a radially loaded bearing. An experimental test-rig was designed such that defects of varying sizes could be seeded onto the outer and inner races of a test bearing. The aim of this investigation was to correlate defect size with specific AE parameters and to ascertain the relationship between the duration of AE transient bursts associated with seeded defects to the actual geometric size of the defect. In addition, the use of AE to detect inner race defects was explored particularly as this known to be fraught with difficulty. It is concluded that the geometric defect size of outer race defects can be determined from the AE waveform.     

窄带随机激励双稳压电悬臂梁响应机制与能量采集研究

具有中心频率的窄带随机振动是一种典型的环境振动，其振动特征与环境的变化密切相关.本文以双稳压电悬臂梁能量采集系统为研究对象，分析系统在不同磁铁间距下的等效线性固有频率特性，以带通滤波器输出一定带宽的窄带随机激励模拟环境振动，研究系统的响应和能量采集特征.研究表明，对于一定带宽的窄带随机激励，一方面系统始终存在一个固定的磁铁间距使其输出达到峰值，另一方面当激励中心频率在一定范围内变化时，系统还分别存在另外两个或一个不同磁铁间距也能使系统输出达到峰值，而且该峰值特性是系统在其等效线性固有频率处诱导双稳或单稳“共振”形成的.研究结果可为具有窄带随机激励特征的振动能量采集提供一定的理论和技术支持.     

同轴回旋行波放大器的理论和数值研究

 给出了一组描述同轴回旋行波放大器中波束相互作用的非线性自洽方程组，对该放大器的运行特性进行了研究。得到：在小信号区，辐射场的增益随同轴波导的内外半径比b/a的增加而增加，达到饱和时的辐射功率仅略有下降；内外导体管壁上的功率损耗密度随b/a的增加而减小。采用电压为90kV，电流为10A，纵向速度零散度为3%，速率比为1的电子束，在34.26～36.78GHz的频率范围内，计算得到了峰值功率约230kW的微波输出，相应的增益和效率分别为46.6dB和25.5%，带宽为7%，内外导体管壁上功率的最大损耗分别为80和56W/cm²。